Yes you would be covered, as the cancellation cover is from the date you paid for your trip and is in respect of the reasons for cancelling the trip as defined by your policy terms/conditions, at the time of the cancellation reason occuring. But you would need to inform the Insurers straightaway and they would obviously look to incur the least possible cost. Depending on the reasons for cancelling, the Insurers may expect the trip dates to be moved, if the trip arrangements allow for this.
If you changed Insurers from May, the new Insurers would pick up the risk from the date your took out the new policy, providing nothing had occured before you took up the policy, which gave rise to the possibility of cancellation of the trip.